A two-person zero-sum stochastic game with a nonnegative stage reward function is superfair if the value of the one-shot game at each state is at least as large as the reward function at the given state. The payoff in the game is the limit superior of the expected stage rewards taken over the directed set of all finite stop rules. If the game has countable state and action spaces and if at least one of the players has a finite action space at each state, then the game has a value. The value of the stochastic game is obtained by a transfinite algorithm on the countable ordinals.

中文翻译：

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超级公平随机游戏

如果每个状态下的单次博弈的价值至少与给定状态下的奖励函数一样大，则具有非负阶段奖励函数的两人零和随机博弈是超级公平的。游戏中的回报是预期阶段回报优于所有有限止损规则的有向集合的极限。如果游戏具有可数的状态和动作空间，并且至少一个玩家在每个状态下具有有限的动作空间，则游戏具有价值。随机博弈的值是通过可数序数的超限算法获得的。